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Physics · Chapter 2: Physical Quantities and Measurement
Base and Derived Quantities
Physical quantities, the seven SI base quantities and their units, and derived quantities such as speed, force, pressure and energy with their units.
Key termRememberExampleWatch out
01Concept
Physics is built on measurement. Anything that can be measured and written as a number with a unit is called a physical quantity. Length, mass, time, temperature and speed are physical quantities. Love, beauty and taste are not, because they cannot be measured.
Every physical quantity has two parts: a numerical value (magnitude) and a unit.
| Quantity | Measured value | Number | Unit |
|---|---|---|---|
| Length of a cricket pitch | 20.12 m | 20.12 | metre (m) |
| Mass of a bag of rice | 10 kg | 10 | kilogram (kg) |
| Time of a T20 over | about 4 min | 4 | minute (min) |
Base quantities
Base quantities are the quantities on which all other quantities are based. They are not defined in terms of other quantities. There are seven base quantities in the SI (International System of Units):
| Base quantity | Symbol | SI unit | Unit symbol |
|---|---|---|---|
| Length | l | metre | m |
| Mass | m | kilogram | kg |
| Time | t | second | s |
| Electric current | I | ampere | A |
| Thermodynamic temperature | T | kelvin | K |
| Amount of substance | n | mole | mol |
| Luminous intensity | I_v | candela | cd |
Derived quantities
Derived quantities are quantities that are defined in terms of base quantities, by multiplying or dividing them. Their units, the derived units, are made from the base units in the same way.
| Derived quantity | Formula | SI unit | In base units |
|---|---|---|---|
| Area | length × breadth | square metre | m² |
| Volume | length × breadth × height | cubic metre | m³ |
| Speed | distance ÷ time | metre per second | m s⁻¹ |
| Acceleration | change in velocity ÷ time | metre per second squared | m s⁻² |
| Density | mass ÷ volume | kilogram per cubic metre | kg m⁻³ |
| Force | mass × acceleration | newton (N) | kg m s⁻² |
| Pressure | force ÷ area | pascal (Pa) | kg m⁻¹ s⁻² (= N m⁻²) |
| Work, energy | force × distance | joule (J) | kg m² s⁻² (= N m) |
| Power | work ÷ time | watt (W) | kg m² s⁻³ (= J s⁻¹) |
| Electric charge | current × time | coulomb (C) | A s |
Some derived units are named after scientists to honour them: newton (Isaac Newton), pascal (Blaise Pascal), joule (James Joule), watt (James Watt), coulomb (Charles Coulomb).
02Real World Examples
Your electricity bill
Your bill counts energy in kilowatt-hours (kWh), a unit of energy made from power × time. 1 kWh = 3,600,000 J.
Tyre pressure
At a petrol pump the air pressure in tyres is shown in psi or bar. Both are units of pressure, a derived quantity; scientists use the pascal.
Cooking gas cylinders
An LPG cylinder is sold by mass (11.8 kg for a domestic cylinder), not by volume, because mass does not change with temperature.
03Practice Questions
Try to answer in your own words first, then open the model answer.
Short questions
Q1.What is a physical quantity? Give two examples.Show answer
Answer
A physical quantity is anything that can be measured and expressed as a number with a unit. Examples: length and mass.
Q2.Differentiate between base and derived quantities.Show answer
Answer
| Base quantities | Derived quantities |
|---|---|
| Not defined in terms of other quantities | Defined in terms of base quantities |
| Only seven | Very many |
| Length, mass, time | Speed, force, density |
Q3.Name the seven base quantities with their SI units.Show answer
Answer
- Length: metre (m)
- Mass: kilogram (kg)
- Time: second (s)
- Electric current: ampere (A)
- Temperature: kelvin (K)
- Amount of substance: mole (mol)
- Luminous intensity: candela (cd)
Q4.Write the SI unit of force in base units.Show answer
Answer
- Force = mass × acceleration
- Unit = kg × m s⁻² = kg m s⁻², which is called the newton (N).
Q5.Show that the unit of pressure, the pascal, equals kg m⁻¹ s⁻².Show answer
Answer
- Pressure = force ÷ area
- = N ÷ m² = (kg m s⁻²) ÷ m²
- = kg m⁻¹ s⁻²
Long questions
Q6.What are base and derived quantities? Explain with the help of a table, and show how the units of speed, density and work are derived.Show answer
Answer
Base quantities are the seven quantities that are not defined in terms of others: length, mass, time, electric current, temperature, amount of substance and luminous intensity. Derived quantities are made from base quantities by multiplying or dividing them.
- Speed = distance ÷ time → m ÷ s = m s⁻¹
- Density = mass ÷ volume → kg ÷ m³ = kg m⁻³
- Work = force × distance → (kg m s⁻²) × m = kg m² s⁻² = joule (J)